G'day Polly.
Thos e truck rachet straps are the way to go. You can get them real cheap on ebay now too. They come in handy for everything and you can keep a heap of them.
The "customers signing" is a tough one. I have asked my insurance company about this and like lawyers, they said that sometimes things aren't worth the paper they are written on!!
This attitude makes it hard for us as frontline workers to differentiate which is covered and which isnt in this grey area.
If you had to do the job, quote it to take alot longer than you'd think. Constantly reasses the tree, take smaller chunks than usual and put extra protection around protected items.
There's no shame in quoting to have it done properly, or just stating its not in your field of work and walking away.